The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to StatisticsVenn, John
Philosophy
The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics
Venn, John
Chance; Logic, Symbolic and mathematical; Probabilities; Science -- Methodology
the explanation adopted, the general result is that fallacies,
as real acts of thought, are impossible within the domain of
pure logic; error within that province is only possibly by a
momentary lapse of attention, that is of consciousness.
13. But though this perfect harmony between subjective
and objective uniformities or laws may exist within
the domain of pure logic, it is far from existing within that
of probability. The moment we make the _quantity_ of our
belief an integral part of the subject to be studied, any such
invariable correspondence ceases to exist. In the former
case, we could not consciously think erroneously even though
we might try to do so; in the latter, we not only can believe
erroneously but constantly do so. Far from the quantity of
our belief being so exactly adjusted in conformity with the
facts to which it refers that we cannot even in imagination
go astray, we find that it frequently exists in excess or defect
of that which subsequent judgment will approve. Our instincts
of credence are unquestionably in frequent hostility
with experience; and what do we do then? We simply
modify the instincts into accordance with the things. We
are constantly performing this practice, and no cultivated
mind would find it possible to do anything else. No man
would think of divorcing his belief from the things on which
it was exercised, or would suppose that the former had anything
else to do than to follow the lead of the latter. Hence
it results that that separation of the subjective necessity from
the objective, and that determination to treat the former
as a science apart by itself, for which a plausible defence
could be made in the case of pure logic, is entirely inadmissible
in the case of probability. However we might
contrive to '_think_' aright without appeal to facts, we cannot
_believe_ aright without incessantly checking our proceedings
by such appeals. Whatever then may be the
claims of Formal Logic to rank as a separate science, it
does not appear that it can furnish any support to the
theory of Probability at present under examination.
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